CAT 1991 Question Paper

From the below given Venn diagram, we can see that F is the conclusion of ADF

All the other options are not logically related.

In ACE : CE are reiterated, A is unrelated to CE

In AEF : All three statements are facts.

In CDF: C and F are reiterated.

Taking only 1st statement into consideration, nothing certain can be said about product Q
Similarly with the only 2nd statement, we have only 1 information about product Q and R.
But considering both statements together we can say with sufficient information that product Q will be more beneficial than product R

Using first statement alone, we won't be able to find distance as insufficient data is there.
Now using second statement alone, we can find distance d as follows:
velocity before engine failure = $$\frac{40}{2}$$ = 20 km/h and after engine failure = 5 km/hr
And we know total time exceeds 45 min.
Hence 2 + $$\frac{d}{5}$$ = $$\frac{40}{60}$$ + $$\frac{40+d}{20}$$
or $$d = \frac{40}{9}$$  km.

Considering 1st statement alone, $$x^2 + x$$ is greater than 50, a two digit number and x is a prime number, then it has to be 7.

On the other hand, we cannot uniquely determine the value of x using statement B alone. Option a) is the correct answer.

As Avg. of 3 quotations is 110, so the sum of them will be 330
Now considering 1st statement alone, if the lowest quotation is 100, then highest can not exceed 129 because then the sum of all three will exceed from 330.
So we can get the answer by considering the first statement only.

Considering first statement only, given information will not suffice to answer that how many people read both Indian express and Times of India as data regarding intersection of all and data regarding number of people reading other 2 newspapers is not given
Now if we consider only second statement then we can answer about people reading both Indian express and Times of India as follows:
Total readers = 200 = 100 (indian express) + 120 (Times of india)  + 50 (Reading none) - Reading both.
So Reading both newspapers = 270-200 = 70

Given information X=3(Y-3)
Now considering first statement alone, we will have following equation:
Y+17 = X
On solving two eq. we can find the value of X.
Hence answer will be A.

Let the side of the smallest square be x.

According to statement 1,$$10x\geqslant 60$$

$$x\geqslant 6$$

According to statement 2, $$7x*6x\leq 1512$$

$$x\leq 6$$

From both the statements x = 6 and the answer can be determined.

Considering the first statement only, we will get radius > 14. Hence, we can't find the value of radius with this information only.
Now considering the second statement only, we will get radius <= 16.​Hence, we can't find the value of radius with this information only.
Now considering both statements simultaneously, we can't find an absolute value of radius.
Hence, answer will be D
 

Considering first and second statement alone, we can't say about time difference as information will not be sufficient.
Now considering both statements together, we can say that if journey duration is of 5 hours and flight departure time is 9:00 a.m., arrival time according to new york will be 2:00 p.m. but it is given that in London, arrival time is 10:00 a.m. Hence, the time difference will be of 4 hours between NewYork and London.